Question

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Emma wants to measure the distance across a river between two large rocks, point A and point B. From B, facing A she turns 90° and walks 79 feet to point C where there is a post. She then continues straight 23 feet to a tree stump at point D. Then, turning 90° again she walks 57 feet to point E so that she is on a straight line between the post C and the rock A on the other side of the river as shown in the diagram. Answer each of the following questions. Show all your work. Five points each. 15 points total. Triangle ABC and EDC are similar triangles. What triangle similarity theorem or postulate will prove this? Why? State which sides and angles you would use to make the argument. Since the triangles are similar the corresponding sides are proportional. Write a proportion you could use to find the unknown distance from A to B using the three known distances. Use “cross multiply and divide” to solve this proportion for the unknown, and state the distance from A to B to the nearest whole foot.

Answer 1

1. Triangles ABC and EDC are similar due to the Angle-Angle (AA) Similarity Postulate. 2. Both triangles are right triangles by construction, this accounts for 1 angle. And angles ACB and DCE are vertical angles to each other and therefore also equal, that accounts for the second angle. So both triangles ABC and EDC have 2 angles with the same measurement and therefore they are similar. 3. Use the relationship between lines CD and CB along with AB and DE. The equation would be CB/CD = AB/ED 79/23 = AB/57 79*57 = 23*AB 79*57/23 = AB 195.7826087 = AB 196 feet is the distance from A to B.